A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie.

PROB. III.

To make an Horizontal Dyal.

DIscribe a Circle on your Plane, as C B D E, and through the Center A of that Circle draw a Meridian line, as B E; cross that line at Right angles with another line, as C D; so shall your Circle be divided into four e∣qual parts: Divide each of these four parts into 90. degrees; so shall the whole be divided into 360. These 360 degrees re∣present the 360 degrees of the Horizon, which a Meridian line drawn through the place of the Sun runs through in every 24. Hours: The motion of which Meridian line through the de∣grees of the Horizon is Regular in a Parallel Sphear; for in e∣qual Time it moves an equal Space throughout the whole Cir∣cle, viz. it will pass through 15. degrees of the Horizon in one Hours Time, (or which is all one) whiles 15. degrees of the E∣quator passes through the Meridian; as was shewed in the last Probleme: But in an Oblique Sphear its motion through the Horizon is Irregular, and that more or less according to the more or less Obliquity of the Sphear: For far Northwards or Southwards you may see this Meridian line pass through 40, 50, yea 60. degrees of the Horizon in one Hours time, viz, whiles 15. degrees of the Equator passes through the Meridian: but in an other Hours time you will scarce have 4 or 5 degrees pass through the Horizon whiles 15 degrees of the Equator passes through the Meridian.

But that you may know the motion of the Sun (represented by this Meridian line) through the Horizon in all Latitudes; E∣levate the Pole to the Elevation of your Place, and chuse instead of a Meridian line drawn through the Place of the Sun the Ver∣nal Colure to be your Meridian line; both because it is most visible; and because from thence the degrees of the Equator are begun to be numbred, so that what so ever decimal degree of the Equator you light on at the Meridian, or else where, you will find its number from that Colure already set down to your hand, without either adding to, or substracting from it. Bring this Colure therefore to the Meridian, and the Index of the Hour Circle to 12. in the Hour Circle. Then turn the Globe

Westwards, and so oft as 15 degrees of the Equator passes through the Meridian, so oft you must examine what degrees of the Horizon the Vernal Colure cuts; and those degrees and mi∣nutes so cut by the Vernal Colure must be found in the Circle C B D E, beginning your account or reckoning at B towards D, and markt with Pricks: through which Pricks you must draw lines from the Center A, and those lines shall be the Hour lines after noon. Then bring the Colure to the Meridian again to find the Fore-noon Hour-lines, and turn the Globe Eastwards, and so oft as 15 degrees of the Equator passes through the Me∣ridian, so oft you must examine what degrees of the Horizon the Vernal Colure cuts; and those degrees and minutes so cut by the Vernal Colure must be found in the Circle C B D E, be∣gining your reckoning from B towards C, and markt with Pricks: through which Pricks you must draw lines from the Center A, and those lines shall be the Fore-noon Hour-lines.

These Hour-lines must be markt from the Meridian line, viz. the line A B, which is the 12 a clock line towards D, with I, II, III &c. till you have numbred to the Hour of Sun set (found by Prob. 7. of the second Book) the longest Day, and from the Meridian line towards C with XI, X. IX, &c. till you have numbred to Sun Rising the longest Day.

The Stile must be placed in the Center and Elevated so many degrees above the Plane, as the Pole is elevated above the Hori∣zon of the Place,

Example of the whole.

I would make an Horizontal Dyal for Londons Latitude: Therefore I E evate the North Pole 51½ degrees above the Hori∣zon, and bring the Vernal Colure to the Meridian, and the Index of the Hour Circle to 12 on the Hour Circle;

And turning the Globe Westwards till the In∣dex points to	1	a clock or till 15 deg of the Equa∣tor pass through the Meridian; I find the Colure cut the Hori in	11. 4	from the Meridian.
2	24. 15
3	38. 4
4	53. ••6
5	71. 6
6	90.

These are the distances of the Hour lines from Noon till 6 at Night: and to these distances on the Plane (counting from B to∣wards

D,) I make pricks; and from the Center I draw lines through these Pricks; and these lines are the Hour lines from 12 to 6 Afternoon. But the Sun in the longest Day shines till past 8 at Night, as you may find by Prob. 48. of the second Book, therefore here wants the two Evening Hour lines; which though they may be found after the same way I found the former, (viz. by continuing the turning of the Globe Westwards) yet that I may the sooner reduce my work to the Plane I Count the num∣ber of degrees between the 6 a clock line and the 5 a clock line in the Circle on the Plane; for the same number of degrees counted from D towards E is the distance of the 7 a clock Hour line from the 6 a clock Hour line; and the number of degrees contained be∣tween the 6 a clock Hour line and the 4 a clock Hour line is the distance of the 8 a clock Hour line from the 6 a clock Hour-line.

[illustration]

Or I need not draw the 7 and 8 a clock Hour lines, till I have drawn the forenoon Hour lines: for then by laying the edge of a

Ruler (that will reach through the opposite side of the Plane) to the Morning 7 and 8 a clock Hour lines, I may by the side of that Ruler draw lines from the Center through the opposite side of the Plane, and those lines shall be the 7 and 8 a clock Hour lines Afternoon.

Having thus all the Afternoon Hour lines, I bring the Vernal Colure to the Meridian again; so shall the Index again point to 12. Therefore, as before I turned the Globe Westwards, so now

turning it Eastwards, till the In∣dex points to	11	a clock, or till 15 deg. of the Equa∣tor pass through the Meridian, I find the Colure cut the Hori. in	11. 40	from the Meridian.
10	24. 15
9	38. 4
8	53. 36
7	71. 6
6	90.

These are the distances of the Hour lines from Noon to 6. a clock in the Morning: and these distances I seek in the Circle of the Plain (counting from the Noon line B towards C) and mark them with Pricks; through which pricks (as before) I draw lines from the Center to the outside the Plane: and those lines shall be the Hour lines.

Or having the distance of all the Afternoon Hour-lines, I have also the distance of all the forenoon Hour lines from the Meridi∣an; as you may see by comparing the two former Tables. For the 1 a clock Hour line Afternoon is equidistant from the Meri∣dian or Noon line with the 11 a clock Hour line before Noon, viz. they are both 11 degrees 40 minutes distant from the Noon line, and the 2 a clock Hour line Afternoon is from the Noon line equidistant with the 10 a clock Hour line Beforenoon; for they are both 24. degrees 15. minutes distant from the Meridi∣an or Noon line: and so all the other Morning Hour lines are di∣stant from the Noon line by the same space that the same num∣ber of Afternoon Hour lines (told from the Meridian on the con∣trary side the Noon line) are distant from the Meridian.

Whence it follows, that since (as aforesaid) the same number of Hour lines after 6 at Night, and before 6 in the Morning have the same distance from the 6 a clock line that the same number of Hour lines before 6 at Night and after 6 in the Morning have from the 6 a clock line; and since the same number of Hour

lines before Noon are equidistant from the Meridian or Noon line by the same space of degrees that the same number of Hour lines Afternoon are; It follows (I say) that having found the distance of the six Hour lines either before or after Noon, you have also given the distance of all the other Hour lines.

If you will have the half Hour lines placed on your Dyal you must turn the Globe till the Index points to every half Hour in the Hour Circle, as well as to the whole, and examine the degrees of the Horizon cut by the Vernal Colure, as you did for the whole Hours; and in like manner transfer them to your Plane.

Having thus drawn all the Hour lines I count from the Noon line 51½ degrees, the Elevation of the Pole here at London; and from the Center A I draw a straight line, as A F through these 51½ degrees, for the Gnomon or Style, and prolong it to the far∣thest extent of the Plane: From this Gnomon or Style I let fall a Perpendicular upon the Noon line, as F G: (this Perpendicular is called the Substile, and this Perpendicular and its Base (which is the Noon line) and Hypothenusa (which is the Gnomon) shall make a Triangle, which being erected upon the Base, so as the Substile may stand Perpendicular to the Plane, the Hypothenu∣sa A F shall be the Gnomon, and be Parallel to the Axis of the World; and cast a shadow upon the Hour of the Day.